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1
Real Estate Investment
Analysis using Excel
Sing Tien Foo
Department of Real Estate
27 May 2016
Graduate Certificate in Real Estate Finance (GCREF) course
2
Website for sample template
• http://www.rst.nus.edu.sg/staff/singtienfoo/
5/27/2016
2
Mathematics of Real Estate
Finance
Quick Recap:
4
Time value of money
• The time value money is the fundamental concept of financial
mathematics
• Money changes in value over time
• Time value is created by the opportunity to invest money at some
interest rates
• Why so? Inflation, risks and productivity of capital
• “Time is money!”
– $1 today is worth more than $1 tomorrow
• “A bird in hand is better than two in the bush”
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Compounding Effects
• What is the value of $1 today at the end of year 2, if the interest rate
of 10% per annum?
• In a simple interest case (no compounding effects):
o FV (Year 2) = $1.0 + ($1 x 10% x 2)= $1.2
• In an annual compounding case:
o Year 1 FV1 = $1.0 x (1.1) = $1.1
o Year 2: FV2 = $1.1 x (1.1) = $1.21
o FV(year 2) = PV x (1+i) x (1+i) = PV (1+i)2 = $1 x (1.1)2 = $1.21
• Difference = $1.21– $1.20 = $0.01 is the COMPOUNDING effects!
• In a half yearly compounding case:
o FV(year 2) = PV x [(1+i/2) x (1+i/2) x (1+i/2) x (1+i/2)] = PV x (1 +i/2)nx2
o FV(year 2) = $1 x (1 + 0.1/2)4 = $1.2155
6
Simple interest versus compound interest
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Simple interest rate
Compounding interest rate
Year
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Future Value of a Lump Sum
• You borrow $1 today and repay in one lump sum 1
year from now. The interest on the loan is 10%.
• What is the amount you owe at the end of one year?
Present, t = 0 1 year
$1
Future value=?10% p.a.
8
Future value formula
• (1+i)n is known as the Future Value Interest Factor
• Notation: FVIFi,n
• When you borrow money from a bank, you are expected to repay the
loan with interest.
• FV=$1.0 x (1+.10)1=$1.10
• Interest over 1 year = ($1.0) x 10% = $0.10
• FV = PV + Interest = $1.10 + $0.10 = $1.10
n
ni iPVFV )1(,
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To be a millionaire!
0
200000
400000
600000
800000
1000000
1200000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Future Value (FV(PV=10,000, i=10%,n))
At n = 49,
FV = 1,067,190.57
At n =20,
FV = $67,275.00
Growth in money over time
10
Effects of interest rate on FV
• What is the Future Value of $10,000 in 20 years’ time if
interest rate is 15%?
• Steps:
o FVIF15%,20 = (1.15)20 = 16.36654
o Future value = $10,000 x (16.36654) = $163,665.4
• What is the future value, if interest rate drops to 10%
o FV10%,20 = $67,725.0
• Exercise: What is the FV in 20 years if interest rate
drops to 5% and 1%?
– FV 5%,20 = $10,000 x (1.05)20 = $26.532.98
– FV 1%,20 = $10,000 x (1.01)20 = $12,201.90
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Interest rate sensitivity
$0
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
$1,000,000
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91
FV
($10,0
00,
i, n
)
Year
5% 10% 15% 20%
>25 >32 >48 >94
12
Interest rate sensitivity
0
50000
100000
150000
200000
250000
300000
350000
400000
1%
2%
3%
4%
5%
6%
7%
8%
9%
10
%
11
%
12
%
13
%
14
%
15
%
16
%
17
%
18
%
19
%
20
%
What is the Future Value of $10,000 in 20-year time at i % interest rate?
i = 20%: $383,376
i =15%: $163,665
i=1%: $12,202
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Exercise: How much is your apartment worth
today?
What is the value of your 99-leasehold apartment bought in 1990 at $200,000, today?
$0
$200,000
$400,000
$600,000
$800,000
$1,000,000
$1,200,00019
90
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Futu
re V
alue
($)
Axis Title
Value of an apartment bought at $200,000 in 1990
2% 4% 6%
$964,469
$341,377
$576,674
14
Present Value formula
• From the FV formula:
• Re-arranging the formula:
• Computing the PV using the above formula:
n
ni iPVFV )1(,
nnii
FVPV
)1(,
763,391$%)0.51(
000,50053%,10
PV
Today, t = 0 5 years
Present value=?
$500,0005.0% p.a.
DISCOUNTING
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Exercise: You plan to replace your car
in 10 years time at $150,000
• Question: If your cash only earns the cpf rate of return of 2.6%, how
much do you need to set aside today?
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
1 2 3 4 5 6 7 8 9 10 11 12
Money set aside today to replace a new car that costs $150k in year 10
2.6% 5.5%
$116,043
$87,815
CONCEPT OF ANNUITY
Part II
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Concept of Annuity
• Instead of a single lump sum payment, we receive a
series of payments made at equal intervals
• The series of payments is known as “Annuities”
• There are two types of annuity
o Annuity Due = payment at the beginning of period
o Regular Annuity= payment at the end of period
• Mortgage payments are usually made at the end of month
• Rental payments are made at the beginning of the month
20
Present Value of Annuity (PFA)
• Suppose you can pay $10,000 for 3 years for a loan
which you take now. What is the loan amount if interest
rate=10% compounded annually?
• $10,000 [(1+0.1)-1 + (1+0.1)-2+ (1+0.1)-3] = $24,868.52
Sing Tien Foo, Dept of Real
Estate, NUS
$10,000$10,000 $10,000
now 1 year 2 years 3 years
Present value?
Year 1 $10,000 * (1 + 0.1)-1 $9,090.909
Year 2 $10,000 * (1+ 0.1) -2 $8,264.463
Year 3 $10,000 * (1+ 0.1)-3 $7,513.148
sum $24,868.52
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Present Value Annuity formula
• Solving the geometric series (Appendix), we can
now define PVAF as
• Since PVAF10%,3=2.4869,
i
iPVAF
n
ni
)1/(11,
869,24$)4869.2(000,103%,10 PVA
i
iANNPVA
n
ni
)1/(11,
22
Exercise: Value of income-generating
property?
• What is the value of a 30-year leasehold industry property that generate a
monthly net rental income of $3,000?
$0
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
1 14 27 40 53 66 79 92 105
118
131
144
157
170
183
196
209
222
235
248
261
274
287
300
313
326
339
352
Cum
ulat
ive
Rent
al ($
)
PV o
f net
rent
al A
nnui
ty
PV of net monthly rental cash flows
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Lecture Outline
• Investing in real estate
• Cash flow pro-forma
• Investment rule – decision criteria
• Case study
• Real Estate Investment Risks
• Summary
• http://www.rst.nus.edu.sg/staff/singtienfoo/
24
Real Estate Investment Analysis
• Motivations for property purchase• Owner occupation versus investment• Reasons for owner occupation:– Pride of ownership– A form of wealth– Consumption of housing services w/o rent
• Perspectives change when purchase is for investment purposes:
– Generate net income
– Capital gains
– Diversification
– Preferential tax benefits
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Operating Cash Flows
Property level unlevered cash flows
Gross Rent or Potential Gross Income
Effective Gross Income
Operating Expenses
Net Operating Income or NOI
Capital Expenditure
Leverage Effects
Debt Service
27
Property level cash flow pro-forma
(unleveraged)
• Operating cash flows (all years):Potential Gross Income = PGI
Less Vacancy Allowance = - v
+ Other Income (eg, parking, laundry) = +OI
Effective Gross Income = EGI
- Operating Expenses = - OE
Net Operating Income = NOI
• Reversion cash flow (disposal of asset):Property Value at time of sale = V
- Selling Expenses (eg, brokerage fees, legal fees) = - SE
Property-level Before-tax Cash Flow = PBTCF
(Net sale value)
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Potential Gross Income (PGI)
• Rental income assuming 100% occupancy
• Important issue: Contract rent or market rent?– Market rent is the most probable rent a property will
command, if placed for lease on the open market
– Contract rent is actual rent paid under the contractual agreement between landlord and tenants
• If a property is subject to long-term leases, contract rent will be used– eg. sale-leaseback leases in some industrial properties
29
Types of Leases
• Straight lease
– “Level” lease payments
• Step-up or graduated lease
– Rent increases on a predetermined schedule
• Indexed lease
– Rent tied to an inflation index, such as Consumer
Price Index, Union wage index, etc.
• Percentage lease
– Rent includes percentage of tenant’s sales
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Effective Gross Income
• Vacancy and collection loss – Historical experience
– Competing properties in the market
– “Natural vacancy” rate• Vacancy rate that is expected in a stable or equilibrium
market
• Miscellaneous income– Car-parking collection
– Signage and advertising space
– vending machines
– Rentals for clubhouse / promotional space
31
Operating Expenses
• Ordinary and regular expenditures necessary to
keep a property functioning competitively
• Fixed expenses that do not vary with occupancy:
– insurance,
– property taxes
• Variable expenses that vary with occupancy:
– utilities
– maintenance and supplies
– service contracts
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Feasibility of investing in the Office building
Case facts:• Net floor area= 200,633 sq ft
• Purchase price = 158.5million• Current market rent = $8.0 psf/month• Rental growth rate = 3% p.a.• Rents are reviewed every 3 years• Service charges = $1.5 psf/month (grow at 1% p.a)• Property tax rate = 10% of gross rent• Terminal value at EOY 5 based on 1% p.a. price growth• Cost of disposal = 1.5%• Expected discount rate is 7%• Assume investor uses 100% equity
Construct a cash flow pro-forma
34
Steps in DCF analysis
• Projecting Cash Flows– Net Operating Income (NOI)
– Terminal Value of Property
– Cash flows can be cash inflows or cash outflows
– Convention: • Cash inflows are positive cash flows (+)
• Cash outflows are negative cash flows (-)
• Investment Measures/Investment Rules– Holding Period
– Discount Rate
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Projection of NOI
Cash Flow Pro-forma:
Year 0 1 2 3 4 5
Equity outlay -$158,500,000
Potential Gross
Rental Income (PGRI) $19,260,768 $19,260,768 $19,260,768 $19,453,376 $19,453,376
Other Operating
Income
Less Vacancy $3,852,154 $3,852,154 $3,852,154 $3,890,675 $3,890,675
Effective Gross Rental
Income (EGRI) $15,408,614 $15,408,614 $15,408,614 $15,562,701 $15,562,701
Operating Expenses/
Service Charges $2,889,115 $2,889,115 $2,889,115 $2,889,115 $2,889,115
Property Tax $1,540,861 $1,540,861 $1,540,861 $1,556,270 $1,556,270
Net Operating Income
(NOI) $10,978,638 $10,978,638 $10,978,638 $11,117,315 $11,117,315
36
Estimating Terminal Value
• Holding Period=5 years
• How do determine terminal/reversionary value?
• 2 methods:
– A simple compounded growth at a constant rate (say 1% p.a.)
Value = $158,500,000 x (1+0.01)5 = $166,585,093
– Going out cap rate, k, and EOY6 NOI
Value = (EOY6-NOI) / k = $12,305,161/7.4% = $166,285,959
• Cost of disposal = 1.5%
• Based on method 1, Terminal value at EOY 5 =
$166,585,093 * (1-0.015) = $164,086,317
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Estimating PV of cash flows
Year 0 1 2 3 4 5
Before tax
equity cash
flow (net): -$158,500,000 $11,123,094 $11,086,980 $11,050,505 $12,379,949 $176,429,058
Present value
factor 1.000 0.935 0.873 0.816 0.763 0.713
PV of equity
cash flow: -$158,500,000 $10,395,415 $9,683,797 $9,020,503 $9,444,604 $125,791,480
Discounting factor = 7%
38
Net Present Value (NPV)
• Net Present Value (NPV) is the discounted cash flows less the initial investment cost (I0)
Where CFt= cash flow at time t; r = total discount rate; and T=holding period
• If I is spread over two periods, say I0 at t=0 and I1
at t=1, then
r
II
r
CFNPV
T
tt
t
1)1(
10
1
0
1 )1(I
r
CFNPV
T
tt
t
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Profitability Index
• Profitability Index (PI) is the ratio of the present value of cash inflows to the initial equity invested (present value of cash outflows).
• PI = PV(inflows)/PV(outflows)
• PI greater than 1 implies that expected return exceeds the discount rate.
40
Internal Rate of Return (IRR)
• The Internal Rate of Return (IRR) is the rate of return required to make the present values of future cash flows equal to the cost of the investment.
T=holding period
T
tt
t
IRR
CFI
1 )1(
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Investment Rules
• Investment measures: Net Present Value (NPV)
Profitability Index (PI)
Internal Rate of Return (IRR)
• If you decide whether to invest or not, then the rule is very simple
• Invest ifNPV >0
PI > 1
IRR > r
42
Leverage
• Definition: Benefits accrued to an investor who borrows money at a rate of interest lower than the expected rate of return on total funds invested in a property
• The term “levered” or “leveraged” refers to the ability of an investor to increase the returns on equity through the use of debt
• Leverage ratio (LR):
Where V = asset value, E = equity value, D = debt value, L/V = Loan to value ratio
VLDV
V
E
VLR
1
1
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46
Funding acquisition with debt
Case 3: acquisition of HSBC building
• Using 40% debt
• At fixed rate of 4% interest rate (monthly
compounding)
• Loan term of 20 years
• Corporate tax 17% (for non-REIT institutions)
• Project the property-level after-tax equity cash
flows
48
Net Present Value using WACC
• To find the value of the project, discount the unlevered
cash flows at the weighted average cost of capital
(WACC):
Where
UCFt = unlevered cash flow before debt at time t
I0 = initial cash outlay
rWACC = weighted average cost of capital = (L/V) rd + (1- L/V) re
L/V = Loan to value ratio
rd= cost of debt
re = equity investor’s return
N = number of investment periods
N
tt
WACC
t Ir
UCFNPV
1
0)1(
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49
Determining WACC
• WACC formula is dependent on the capital structure at
the firm level, not at the project level
• Let re = levered equity return; rd =c ost of debt; =
corporate tax rate;
• Total Capital V = E (equity) + D (Debt)
• For a firm with a capital structure of D/V = 0.4 E/V = 0.6,
and re = 10% and rd = 4% and = 17%
edWACC rDE
Er
DE
Dr
)1(
%328.7%106.0%)171(%44.0 WACCr
51
Capital Expenditures (CAPEX)
• Expenditures that materially increase value of a structure or prolong its life:– Roof replacement
– Additions and alterations
– HVAC Replacement
– Resurfacing of parking areas
– Tenant improvements
• Estimating CAPEX:
– Sinking fund: An amount invested annually that compounds to the needed CAPEX in a future year.
– Straight-line: For an expenditure n years away, an amount equal to the needed CAPEX divided by n.
– Actual expenditures: The actual amount expected in each year of the expected holding period
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52
Effects of capex on NOI
Source: Fisher (1995), Real Estate Finance
53
Derivation of NOI (revisited)
• Operating cash flows (all years):Potential Gross Income = PGI
- Vacancy Allowance = - v
+ Other Income (eg, parking, laundry) = +OI
Effective Gross Income = EGI
- Operating Expenses = - OE
Net Operating Income = NOI
- Capital Expenditures = - C
Property-level Before-tax Cash Flow = PBTCF
• Reversion cash flow (disposal of asset):Property Value at time of sale = V
- Selling Expenses (eg, broker) = - SE
Property-level Before-tax Cash Flow = PBTCF
(Net sale value)
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54
Net Operating Income (NOI) and
Capital Expenditure (Capex)
• Capex
– Reserve for replacements
– Tenant improvement
– Leasing commissions
• Above-line or below-line approach
Above Line:
EGI
- OE
- CAPX
= NOI
Below Line:
EGI
- OE
= NOI
- CAPX
= Net Cash Flow
55
Asset Enhancement Initiatives (AEI)
Case 2: The Extension of IMM Building
• CAPITAMALL Trust (CMT) acquired the IMM Building in Jurong for $264.5 million in 2003
• IMM completed a major revamp in Dec 2007 by building a three-storey annexed block on the ground level open-air carpark
• The first floor of the new block will consist of retail space while the parking space will be moved to the upper floors.
• CMT expects IMM purchase to raise returns.
• By Vladimir Guevarra.
• 14 May 2003
• Straits Times
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56
Some background facts of IMM AEIs
• Major asset enhancement works at IMM were completed on
schedule in December 2007.
• A new two-storey retail extension block with over 20,000 sq ft of
retail space was created
• Following the successful revamp, average rental at IMM increased
34.3%, from S$7.99 per sq ft to S$10.73 per sq ft per month
• An incremental rental revenue of S$13.3 million per annum.
• Based on a capital expenditure of S$92.5 million, the entire scope of
work contributed to an incremental NPI of S$10.0 million per annum
and achieved an ungeared ROI of 10.8%.
• Estimate the investment return of the AEIs
57
Property details & some assumptions
(hypothetical)
As in 2003 Major AEI in 2007
Net Lettable Area (retail) 877,252.0 sq ft Additional 20,000 sqf
Number of Tenants 510 About 600
Car Park Spaces 1300 1300
Title 30 years Leasehold term
wef 23 January 1999
No change
Acquisition Price (2003 S$264.5 million
Capex (2007) $92.5million
Occupancy 76.7% 85%
Effective Gross Rental Income S$45.0 million Incremental = $13.3million
Operating Expenses (including
property tax)
$23.0 million Incremental = $3.3 million
Rental growth rate 2% 2%
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58
Avoiding Pitfalls in DCF applications
• “GIGO” – Garbage in garbage out
• Common mistakes
– Rental / income growth assumption is too high
– Capital improvement and going-out cap rate projections are too low
– Discount rate is too high
• Errors are hidden in the DCF model, which may create false expectation for investors in the long-run
• Consequences of the mistakes
– Unrealistic expectations
– Long-run undermining credibility of DCF methodology
· Read the “fine print”.
· Look for “hidden assumptions”.
· Check realism of assumptions.
Thank you
59
References
• Ling, D.C. and Archer, W.R. (2005), Real Estate
Principles: A Value Approach, McGraw Hill
• Brueggeman, W.B. and Fisher, J.D. (2011), Real
Estate Finance and Investments, 14th Edition,
McGraw Hill
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